With all this in mind, let's introduce some notation. We want to say that \(8\) and 23 are basically the same, even though they are not equal. It would be wrong to say \(8 = 23\text{.}\) Instead, we write \(8 \equiv 23\text{.}\) But this is not always true. It works if we are thinking division by 5, so we need to denote that somehow. What we will actually write is this:
which is read, “8 is congruent to 23 modulo 5” (or just “mod 5”). Of course then we could observe that